Question

(15 Points 15. First Order Lead/Lag Compensation Consider first-order digital compensation for a second-order plant given by: 1 G (s) = (s It has a compensator given (in the s-domain) by: 1)(s10) 3004(s1) C(s) = S42 We recall that digital compensator may be thought of a continuous equivalent, given by: K(z - A) (k(s a = Z D(z) = z B Sb Where A e-al and B = e-DT (and K is distinct from k). Please assume 50 Hz, ZOH sampling throughout A. Using D(z) above, what is an expression for K when s 0 (i.e. the DC gain)? B. Using the controller C(s) and the result in (A), what are K, A and B such that we have unity gain at DC? C. Determine the closed-loop (negative) unity feedback continuous-time transfer function, H(s), for the controller and plant together and very briefl descri procedu (and/or give ıdocode) to D. determine H(z). E. A possible step response for H(s) (i.e. Part C) is given below. For this case, please sketch the step response of H(z) Hint: Please remember to answer in the answer booklet] Step Response of H(s) 1.2 0 8 0.6 0.4 0.02 0.06 0.08 0.14 n.04 0.1 0.12 0.16 0.18 0.2 Time (seconds)

Full working and explanation please

Answer 1

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